Question

The derivative of $2x+3y=\sin y$ is

• A. $\frac{2}{\cos y}$
• B. $\frac{2}{\cos y+3}$
• C. $\frac{2}{\cos y-3}$
• D. None of these

Answer 1

Answer: (C)

Given, $2x+3y=\sin y$
On differentiating both sides w.r.t. $x$, we get
$\frac{d}{dx}(2x+3y)=\frac{d}{dx}(\sin y)$
$\Rightarrow 2+3\frac{dy}{dx}=\cos y\frac{dy}{dx}$
$\Rightarrow 3\frac{dy}{dx}-\cos y\frac{dy}{dx}=-2$
$\Rightarrow (3-\cos y)\frac{dy}{dx}=-2$
$\Rightarrow \frac{dy}{dx}=\frac{2}{\cos y-3}$